In Janet Price wrote:
I have heavy clay soil with several soggy areas and am looking for an
inexpensive way to eliminate or reduce them.

I have the exact same problem, and my plan is not to try and eliminate
those spots, but live with them by planting things that don't mind wet
soil. These spots aren't permanently wet, they just drain slowly after
heavy rain, so I'm looking for flood-tolerant plants like River Birch,
Sweet Bay Magnolia, Itea, Cypress, Clethra. If that approach works for
you, it might save you some time, money, and frustration.